How much data do you want for your progress? Quantitative History and the Study of Social Problems

Nathan Alexander, PhD

Howard University

Framing our time.

  • A bit about me.

  • Our lab, the Quantitative Histories Workshop.

  • How much data do you want for your progress?

A bit about my ancestors, my journey, teachers, and students.

A stolen people on stolen land.

My ancestors come from the coast of the Carolinas (NC and SC), where enslaved Africans entered what is now known as the United States. I was born in Charlotte, NC. Meaning that, over time, like many other Black families, there was little movement beyond the South.

The Carolinas, from the Equal Justice Initiative (2026)

My family has very few historical records of our ancestors.

My maternal ancestors circa 1900

In 1971, Charlotte, NC, became a national model for school desegregation through court-ordered busing following the landmark Swann v. Charlotte-Mecklenburg Board of Education Supreme Court ruling. In 1989, at the age of 5, I would become part of this desegregation plan.

Busing as a result of Swann v. Charlotte-Mecklenburg Board of Education

I was raised in a public housing project in South Charlotte, known as Boulevard Homes in the 90s. These projects were just one exit, a literal two-minute drive, from the Charlotte Airport. This meant that we were in a food and transportation desert next to a busy roadway, Billy Graham Parkway, separated only by a single line of trees.

Boulevard Homes Public Housing Project, Charlotte, NC

Despite our economic conditions, my parents supported our learning and well-being.

My 5th birthday party with my sisters and cousins.

By mere luck, I would be bused to Selwyn Elementary, the #1 elementary school in Charlotte at the time. For context, the surrounding median home value as of Feb. 2026 is $2,524,5001.

Selwyn Elementary School

The mathematics of opportunity.

As a result of busing, I would have access to educational resources that my first cousins, who lived in the housing project across the street, known as Little Rock in the 90s, would not be able to access. Their bus took them to a different school on the other side of Charlotte.

I recently published a paper on this issue in the Journal of Negro Education.

  • Alexander, N. N. (2024). Measuring School Desegregation: A Critical Quantitative Replication. The Journal of Negro Education, 93(3), 318-331.

In this paper, I discuss a mathematical model used to measure segregation, known as the Index of Dissimilarity, and its relationship to the 70th Anniversary of the 1954 Brown v. Board of Education of Topeka Supreme Court decision. More on this later…

\[ D = \frac{1}{2} \sum_{i=1}^n \left| \frac{b_i}{B} - \frac{w_i}{W} \right| \]

For the love of mathematics.

My first club at Alexander Graham Middle School

I would then spend a summer in Boone, NC with the Summer Ventures Program. It was here that I decided I wanted to be an architect, after spending most of my time building housing structures with balsawood.

Summer Ventures Program

The transition to my undergraduate studies.

Phillips Hall, UNC Department of Mathematics

@UNC - Double major in mathematics and sociology.

I was the only Black math major in the department.

I would fall in love with coding in my statistics courses in sociology.

UNC Math Department Newsletter

My 1st math course at UNC

MATH 89H - First Year Honors Seminar – Fractals. Taught by Sue Goodman, Topologist.

We spent the first-half of the term making connections to the real world; most literally, going outside to observe tree bark, patterns in the grass, reading books (e.g., The Labryinth), and writing “fractal” poems.

Fractal Geometry

During the second-half of the term, we would formalize our observations. Starting with the Mandelbrot set and extended it to similar forms, such as the Julia set. A Julia set is a bunch of fractals that are similar to the Mandelbrot Set. It is a set defined given a rational function, \(J(f)\), such that all nearby values behave similarly when the function is repeatedly iterated.

A Julia Set

My 2nd math course at UNC

Calculus of Functions of Several Variables

My second math course was in stark contrast to what I had imaged the rest of my mathematical experiences would be in college. I would spend nearly every day after class with Dr. Petersen, building my first honest relationship with a professor.

Karl Petersen, Ergodic theory

My job as a grader and teaching assistant

UNC Math Help Center

Differential Equations and Linear Algebra for Applications

James Damon, Singularity theory

Noberto Kerzman (1943-2019), Complex analysis

Introduction to Real Analysis

Dr. Assani, a Beninese mathematician, joined the UNC mathematics department in 1988 but, for racist reasons, was turned down for tenure. He appealed through the courts, won his case and gained tenure in 1995, and was promoted to full professor one year later. In doing so he became the first Black tenured associate mathematics professor and the first Black full mathematics professor at UNC, as well as the only mathematician there to be promoted from associate to full so quickly (Mathematicians of the African Diaspora, 2014)

Idris Assani, Ergodic theory

Study Abroad at the National University of Singapore

I was selected as part of a first group of students to travel to the National University of Singapore as part of a new exchange program. Given the newness of the program, we would travel early to meet students in Singapore, whose families would serve as our hosts over the holiday break, and they would then leave for UNC at the start of the spring.

NUS

My favorite course at the National University of Singapore

In The Horror of the Other, a humanities and social science elective, we examined the concept of othering. I would write my first interdisciplinary mathematical analysis of social science concepts using the ideas of equivalence relations, sameness, and difference.

Chitra Sankaran, NUS, Humanities and Social Sciences

The Others

Junior Year back @ UNC

At Carolina (UNC), the Department of Mathematics is next door to the School of Education. When I returned my junior year, I would meet Dr. Carol Malloy, a famous mathematics educator and faculty member in the School of Education.

Carol Malloy, 1944-2015, UNC School of Education

Lead Math Tutor at UNC’s Upward Bound Program

As a result of meeting Dr. Malloy, I would be asked to become the lead tutor for UNC’s Upward Bound program. This would be on top of my job as a TA and grader in the mathematics department. I would tutor undergraduates during the week and teach mathematics to high school students on Saturday mornings.

UNC Upward Bound Program

Master of Arts in Teaching @ New York University

I would accept a scholarship to NYU to learn how to teach mathematics. While in New York, I would study under Dr. Karen King, who taught me theories of education and the pedagogy of mathematics. Dr. King would challenge me to create culturally relevant math lessons.

Karen King, 1971-2019, MAT advisor

Student Teaching

Pre-service teachers are required to complete about 200 hours of student teaching in a local high school. I was placed at a school for recent Chinese immigrants in the Lower East Side (LES) of New York at the LES Community School. Here, I created my first ethnomathematics unit plan.

Camping trip with students from Lower East Side Community School, 2008

Teacher of Record

My first teaching experience as the teacher of record would be in Bedstudy, Brooklyn, NY at a middle school for Boys. I would move from Brooklyn to Harlem to teach at the Harlem Children’s Zone. I would be tapped by the COO, George Khaldun, to support org-wide statistical analysis with external, mostly white, business consultants. Given their lack of contextual knowledge, I became interested in getting a PhD to combat their deficit narratives of the youth and families.

TRUCE @ Harlem Children’s Zone

PhD program in Mathematics and Education @ Columbia University

I would go on to study in the Program in Mathematics at Teachers College, Columbia University. The first program of its kind in the country. In this program, 75 credit hours over 5 years, we take PhD courses and qualifying exams in mathematics (I completed exam requirements in Topology/Geometry, Statistics & Probability Theory, and Analysis) and advanced theory courses in mathematical education. This allows us to work in both departments of mathematics and schools of education.

Teachers College, Program in Mathematics

Doctoral work as a Gradaute Research Assistant

I studied under Dr. Erica Walker, who studies the histories and social networks of Black mathematicians. As her graduate assistant, I would begin my initial foray into archival research as she completed her book, Beyond Banneker.

Erica Walker, my PhD advisor

Beyond Banneker by Erica Walker

Postdoctoral work at UC Berkeley

As I transitioned out of my PhD program, I would move to the Bay Area, CA and become a visiting scholar in the Department of Mathematics and School of Education at UC Berkeley.

Visiting Scholar in the Department of Mathematics at UC Berkeley

I would also teach high school arts students at the Oakland School for the Arts. I was allowed to develop an interdisciplinary curriculum focused on art, history, and mathematics.

Students in my geometry class at OsA

Working on a math \(\times\) dis/ability unit project

Department of Mathematics @ Morehouse College

I became a visiting professor in the Department of Mathematics at Morehouse College. In this role, I focused on supporting students during their transition from high school to college, thinking largely about my first-year experiences in mathematics as an undergrad at UNC.

My first class at Morehouse College

Youth Participatory Action Research (YPAR) in Mathematics

I also helped launch a summer research program at Morehouse for local high school students. I would teach a first course on abstraction, mathematics, justice. This program, the Summer Math and Science Honors Academy (SMASH) is supported by the Kapor Foundation.

Summer Math and Science Honors Program at Morehouse

SMASH Student Project

SMASH Student Project

Quantitative Histories Workshop

curriculum & software development collective

and

research lab

Research Problem

Increasingly complex problems require complex tools.

Computational tools support interdisciplinary thinking.

Research Problem

Increasingly complex problems require complex tools.

Computational tools support interdisciplinary thinking.

Research Problem

Increasingly complex problems require complex tools.

Sub-disciplinary tools require interdisciplinary thinking.

How might information theories inform interdisciplinary curriculum and software development?

Information theory

Information theory is a branch of applied mathematics and computer science that deals with the quantification, storage, transmission, and manipulation of information. We take an abstract approach to our study of information.

  • Information theory seeks to measure the amount of information contained in a message or signal and how efficiently it can be transmitted or stored.

  • In this way, our projects define information using a curricular perspective.

  • Namely, how might faculty and educators leverage computation and quantification to transmit information efficiently while maintaining the roots of complex theories and concepts?

Quantitative history

Historie Quantitative by Pierre Chaunu

Mathematical sociology

Journal of Mathematical Sociology

Curriculum and software development

Design, development, implementation, and evaluation of computational curricular materials

Research projects

  • ECHO: Education, Community, and Health Observations

    • Information and spatial segregation
  • Quantifying state violence

    • Prisons, a history of the U.S.

    • Policing, power and punishment.

    • The divided states of america: Politics and the development of an empire

  • Statistics and data science education

    • Teaching statistical learning and mathematical modeling

    • Computation and adult learning

  • Maintaining complex theory in quantification

    • Theories and conceptions of race and racism

Research projects

  • ECHO: Education, Community, and Health Observations

    • Information and spatial segregation
  • Quantifying state violence

    • Prisons, a history of the U.S.

    • Policing, power and punishment.

    • The divided states of america: Politics and the development of an empire

  • Statistics and data science education

    • Teaching statistical learning and mathematical modeling

    • Computation and adult learning

  • Maintaining complex theory in quantification

    • Theories and conceptions of race and racism

Project overview: Spatial information and racial isolation

Washington Post map on Fair Cities Act (1968)

Information and spatial segregation

How have histories of racial segregation informed education, community, and health outcomes?

Chodrow (2017), examines residential segregation using a taxonomy of smoothing-based segregation metrics, we consider key historical components and markers in the development of a history of “dividing walls”.

  • Historical legacies of injustice. “The 1968 [Fair Cities] Act expanded on previous acts and prohibited discrimination concerning the sale, rental, and financing of housing based on race, religion, national origin, sex, (and as amended) handicap and family status.” (US Housing and Urban Development, n.d)

  • Traditional modeling approaches. What has been done more recently and historically?

  • Modern computational tools. What new (grounded) theoretical insights can be identified?

A theory and history of dividing walls

Geometric approach

We adopt a topological model for spatial segregation on a geographical area, \(G\) to develop a theory of dividing walls.

Builds on the topological and topographical work of Short (2011).

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with neighborhood units

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with neighborhood units

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with wall dividing neighborhood units

Is there a dividing wall for an island with coastal towns?

Island with coastal towns

Is there a dividing wall for an island with coastal towns?

Minimal configuration

Theorem 2. Alternating configurations of towns do not have a dividing wall, whereas non-alternating configurations of towns do have a dividing wall.

Alternating configuration (left) and non-alternating configuration (right).

Algebraic approach

We then develop a algebraic modeling approach using methods from mathematical sociology.

Segregation indices

  • Dissimilarity index: Measures the proportion of one group’s population that would need to move to achieve an even distribution across all areas. It ranges from 0 to 1, with higher values indicating greater segregation.

  • Isolation index: Measures the extent to which members of a particular group are surrounded by others from the same group. It represents the percentage of people from a specific group who would need to change neighborhoods to achieve an even distribution. Higher values indicate higher isolation and segregation.

Algebraic approach

We then develop a algebraic modeling approach using methods from mathematical sociology.

Segregation indices

  • Exposure index: Measures the extent to which members of one group are exposed to members of another group. It quantifies the likelihood that a randomly selected individual from one group will encounter individuals from another group. Higher values indicate higher exposure and lower segregation.

  • Concentration index: Measures the extent to which a particular group is concentrated in specific areas or neighborhoods. It reflects the degree of clustering or dispersion of the group’s population across geographic units.

  • Gini index: Measure of income inequality, but it can also be adapted to measure residential segregation. It provides a summary measure of the overall distribution of different groups across neighborhoods.

## Racial isolation from an algebraic geometry approach

Horizontal configuration.

## Racial isolation from an algebraic geometry approach

Vertical configuration.

Index of Dissimilarity

\[ D = \dfrac{1}{2} \sum_\limits{i=1}^n \bigg| \text{Proportion of Black units} - \text{Proportion of non-Black units} \bigg| \]

  • \(n\) is the number of neighborhoods in a geographic region,

  • \(b_i\) is the number of Black household units in neighborhood \(i\),

  • \(B\) is the total number of Black household units in the geographic region,

  • \(w_i\) is the number of non-Black household units in neighborhood \(i\),

  • \(W\) is the total number of non-Black household units in the geographic region.

Index of Dissimilarity

\[ D = \dfrac{1}{2} \sum_\limits{i=1}^n \bigg| \dfrac{b_i}{B} - \dfrac{w_i}{W} \bigg| \]

- $n$ is the number of neighborhoods in a geographic region, 
  • \(b_i\) is the number of Black household units in neighborhood \(i\),

  • \(B\) is the total number of Black household units in the geographic region,

  • \(w_i\) is the number of non-Black household units in neighborhood \(i\),

  • \(W\) is the total number of non-Black household units in the geographic region.

Computational approach

Teaching computational methods and open source tools makes for efficient and accurate learning. In about 5 lines of code, there is an immediate intersection of theory and computation.

Here we use the tidycensus() package to gather various metrics.

Prisons

The U.S. Bureau of Justice Statistics maintains records of federal and state prison populations1.

Prisons

To support our framing of contemporary data, we take on an historical view.

Federal racialization data

State racialization data

Federal and State racialization data

Broad Implications

  • K-12 teaching and learning

    • This also exposes students to a diversity of problems and methods to solve those problems.
  • Computationally-focused research and training in higher education

    • Provides an equitable pathway and entry into “high information, high density” conversations.
  • Industry and professional organizations

Gratitude for your time.

Abstract

We explore how multidimensional measures of local communities – such as those provided by the Census Community Resilience Estimates (CREs) – can be used to frame and model dynamic changes in neighborhood communities using an intersectional lens.

We build on prior research inspired by work on the United States as a “Patchwork Nation.”

Quantitative Histories Workshop

curriculum & software development collective

and

research lab

Project background: Information and spatial segregation

Information and theory

Information theory is a branch of applied mathematics and computer science that deals with the quantification, storage, transmission, and manipulation of information.

We take an abstract approach to our study of information.

  • Information theory seeks to measure the amount of information contained in a message or signal and how efficiently it can be transmitted or stored.

  • This project seeks to define information using a critical computational perspective.

  • Namely, how might we leverage computation and quantification to transmit information efficiently while maintaining the roots of complex theories and histories?

Mapping Single Dimensions

Theoretical framework: A Patchwork Nation

If you pay attention to the complexity of the USA, its diversity and differences you soon realize that the ways we try to understand it – red and blue, Northeast and Midwest – are too simplistic. They are inadequate and misleading.” -Patchwork Nation Project

Theoretical framework: A Patchwork Nation

  • Boom Towns: Rapidly expanding communities

  • Campus and Careers: Areas with a significant presence of higher education institutions

  • Immigration Nation: Areas with high concentrations of immigrant populations

  • Industrial Metropolis: Large urban areas with a strong industrial base

  • Emptying Nests: Communities with an aging population

  • Minority Central: Areas with large minority populations

  • Monied Burbs: Affluent suburban areas

Analytic framework: Community Resilience Estimates

  • The Census Community Resilience Estimates (CRE) data sets were developed to assess the social vulnerability and resilience of neighborhoods in response to disasters or shocks.

    – Households with an income-to-poverty ratio less than 130%

    – Less than one individual living in the household is aged 18–64

    – Household crowding, defined as more than 0.75 persons per room

    – Households with limited education

    – No one in the household is employed full-time year-round

    – Individual with a disability posing a constraint to significant life activity

    – Individual with no health insurance

    – Individual aged 65 or older

    – Households without a vehicle

    – Households without broadband internet access

Analytic framework: Community Resilience Estimates

  • CRE estimates are a measure of the capacity of individuals and households within a community to absorb, endure, and recover from external stresses.

  • The CRE data combine American Community Survey (ACS) and the Population Estimates Program (PEP) data to identify social and economic vulnerabilities by geography.

  • There is a nice CRE Interactive Tool that allows for a quick overview of local contexts.

cre_correlates_dc <- get_acs(
  geography = "tract", state = "DC", year = 2023, survey = "acs5",
  variables = c(
    median_income = "B19013_001",       # Median household income in the past 12 months
    poverty_rate = "B17001_002",        # Number of people below poverty level
    unemployment_rate = "B23025_005",   # Number of civilians (16 years and over) unemployed
    no_health_insurance = "B27010_033", # Number of people with no health insurance coverage
    educ_less_than_hs = "B15003_002",   # Population 25 years and over with less than 9th grade education
    median_age = "B01002_001",          # Median age
    housing_cost_burden = "B25070_010", # Housing units spending 50% or more of income on rent
    no_vehicle = "B08201_002",          # Households with no vehicle available
    black_population = "B02001_003",    # Black or African American alone population
    median_rent = "B25058_001"),        # Median contract rent
  summary_var = "B02001_001",           # Total population (for calculating proportions)
  output = "wide", geometry = FALSE)

Dimensionality in Spatial Models

Model development

– Base spatial model formulation: \[ \boldsymbol{y} = \boldsymbol{X}\beta + \tau + \epsilon \]

  • \(\boldsymbol{y}\) is a \(n\) x \(1\) response vector

  • \(\boldsymbol{X}\) is a design matrix that contains explanatory variables

  • \(\beta\) represents fixed effects coefficients

  • \(\tau\) denotes spatially dependent random errors

  • \(\epsilon\) represents independent random errors

Dimensionality in Spatial Models

Model development

Response vector structure (\(\boldsymbol{y}\)):

\[ \begin{align} \boldsymbol{y} &= \begin{bmatrix} y_{1} \\ y_{2} \\ \vdots \\ y_{n} \end{bmatrix} \end{align} \]

  • Each element, \(y_i\), represents the observed response at a neighborhood’s location \(i\)

  • These are ordered by adjacency relationships to preserve the geographical context

  • Also, review of distributions, spatial autocorrelation (i.e., \(Cov(y_i, y_j)\)), and decomposition

Dimensionality in Spatial Models

Model development

Design matrix of explanatory variables structure (\(\boldsymbol{X}\)):

\[ \boldsymbol{X} = \begin{bmatrix} 1 & x_{1, 1} & \ldots & x_{1, p} \\ 1 & x_{2, 1} & \ldots & x_{2, p} \\ \vdots & \vdots & \ddots & \vdots \\ 1 & x_{n, 1} & \ldots & x_{n, p} \\ \end{bmatrix} \]

  • First column is the intercept term

  • Subsequent columns represent \(p\) explanatory variables

  • Each row corresponds to a specific neighborhood’s covariates

Dimensionality in Spatial Models

Sample design matrix of explanatory variables

\[ \boldsymbol{X} = \begin{bmatrix} 1 & 65,000 & 0.62 & 3,200 \\ 1 & 28,000 & 0.32 & 5,100 \\ \vdots & \vdots & \vdots & \vdots \\ 1 & 127,000 & 0.75 & 6,840 \\ \end{bmatrix} \]

  • Column 1 is the expected value of \(\boldsymbol{y}\) when all other predictors are zero

  • Variable 1 (column 2) as median income

  • Variable 2 (column 3) as the proportion of residents with a high school diploma

  • Variable 3 (column 4) as population density (residents/sq. mi)

Information and spatial segregation

Model selection

There are multiple models for consideration:

Spatial regression using intersectional interactions

Structural Equation Modeling (SEM) with CRE components

Multilevel Analysis of Individual Heterogeneity and Discriminatory Analysis (MAIHDA)

  • Evans et al. (2024). A Tutorial for Conducting MAIHDA. Population Health, Vol. 26, 101664

  • Combines intersectional stratification with neighborhood-level clustering

  • Models individuals nested within: Intersectional strata (e.g., low-income Black men), community typologies from framework (e.g., Patchwork Nation) classifications

Overview

Case analysis: Health

Hypertension

Hypertension, also known as high blood pressure, is a condition in which the force of blood pushing against the walls of the arteries is consistently too high.

The condition is a compounding health concern in the United States.

Between 2017-2020, an estimated 115.3 million US adults had high blood pressure, representing up to 45% of the adult population.

The prevalence of high blood pressure fluctuations over time:

  • Between 1999–2000, high blood pressure was highest at 47.9%
  • It reached its lowest points between 2009-2010 and 2013-2014 at 43%
  • As of 2017-2020, high blood pressure had a national average of around 48%

Hypertension rate in the US

Time Trend of Hypertension Mortality Rates Over Time in the US

Comparative rates in the DMV

Bar chart of Hypertension Morbidity Rates in Proximal States

CRE and hypertension morbidity

While the Community Resilience Estimates (CRE) do not directly measure hypertension, there are several indirect connections between hypertension and community resilience:

  • Health Insurance: One of the CRE risk factors is lack of health insurance. Individuals without health insurance are less likely to receive regular blood pressure screenings and treatment for hypertension.

  • Socioeconomic Factors: The CRE includes factors like poverty and employment, which are known to influence hypertension rates.

  • Education: Limited education is a CRE risk factor. Lower educational attainment is associated with higher rates of hypertension.

  • Age: The CRE considers households with individuals aged 65 or older as a risk factor. Hypertension increases with age, making older populations more vulnerable to its effects.

CRE and hypertension morbidity for DC

Correlation Matrix of Hypertension and Socioeconomic Factors
Variables
hypertension_rate POVERTY_RATE UNEMPLOYMENT_RATE EDUCATION_RATE
hypertension_rate 1.000 0.240 0.565 -0.706
POVERTY_RATE 0.240 1.000 -0.152 -0.006
UNEMPLOYMENT_RATE 0.565 -0.152 1.000 -0.642
EDUCATION_RATE -0.706 -0.006 -0.642 1.000

Racial Differences and Hypertension Morbidity for DC

Correlation Matrix of Hypertension Rate and Racial Demographics in DC
Variables
hypertension_rate white black asian native hawai_pac
hypertension_rate 1.000 -0.876 0.898 -0.673 0.098 -0.113
white -0.876 1.000 -0.966 0.567 -0.103 0.112
black 0.898 -0.966 1.000 -0.650 0.074 -0.124
asian -0.673 0.567 -0.650 1.000 -0.050 0.163
native 0.098 -0.103 0.074 -0.050 1.000 -0.031
hawai_pac -0.113 0.112 -0.124 0.163 -0.031 1.000

Hypertension and CRE

Race and Ethnicity

We are also developing a dashboard for internal use to automate some processes.

US Census Demographics Data Dashboard

Political analysis

Examining the impact of broader political shifts on neighborhood measures.

  • Project title: Examining Polling Location Changes After The Shelby County Decision: How a Lack of Federal Oversight Impacts Poll Accessibility in Black and Brown Communities

  • Abstract: Since the Supreme Court’s Shelby Decision in 2013, states are no longer required to have polling station changes or closures federally reviewed. Given that over 1600 polling locations have been closed or changed since 2013, we ask what factors contribute to these polling location changes and closures? We examine the driving forces behind these changes, and use Census data to determine what implications these polling location changes may have on accessibility in communities of color.

Special Thanks

Research assistants: Myles Ndiritu (Morehouse College), Zoe Williams (Howard University), Kade Davis (Morehouse College), Amari Gray (Morehouse College)

Lab manager: Lyrric Jackson (Spelman College)

Funding: Alfred P. Sloan Foundation, AUC Data Science Initiative, Data.org

Partners: The Carpentries

References

Chinni, D., & Gimpel, J. (2010). Our Patchwork Nation: The Surprising Truth about the “Real” America. Gotham Books.

Evans, C. R., Leckie, G., Subramanian, S. V., Bell, A., & Merlo, J. (2024). A tutorial for conducting intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA). SSM - Population Health, 26, Article 101664. https://doi.org/10.1016/j.ssmph.2024.101664.

U.S. Census Bureau. (2024). Community Resilience Estimates. Retrieved March 26, 2025, from https://www.census.gov/programs-surveys/community-resilience-estimates/about.html.